The online reporting method is only available from 15 days before to eight days before. Bottom line is if you've been here for 90 consecutive days you report, period.
You could send in all your passport pages preemptively with the scan of your Vietnam visa, entry stamp, and accommodation booking. All that after you've crossed into Vietnam of course and then submit your application. worst case scenario they ask for more recent photos.
You're both likely on extensions and not visas, should be pretty straightforward to change the reason for your extensions. As always contact your local immigration office and ask for the handout and procedures to change reason for extension.
Your old passport is invalid once the new one is issued, it's only purpose now is to confirm the same passport number the visa was originally issued to is yours. All stamps will be in the new valid passport. Printout a copy of your DTV as well for the passport control officer.
Anonymous participant 6 months is cutting it close these days. Times have changed and requirements are getting somewhat stringent. Possibly a cover letter along with your application stating your reasons for visiting, why this course , general interest in why you love Thailand, plans after finishing the course, and what you'll do with the remaining 4 years of the visa.